The fundamental theorem of finite fields: a proof from first principles

The fundamental theorem of finite fields: a proof from first principles

A mathematics student's first introduction to the fundamental theorem of finite fields (FTFF) often occurs in an advanced abstract algebra course and invokes the power of Galois theory to prove it. Yet the combinatorial and algebraic coding theory applications of finite fields can show up early...

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Veröffentlicht in:arXiv.org 2021-08
Hauptverfasser: Chavez, Anastasia, O'Neill, Christopher
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Sprache:eng
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Algebra
Binary system
Combinatorial analysis
Fields (mathematics)
First principles
Numbers
Students
Technical education
Theorems
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description A mathematics student's first introduction to the fundamental theorem of finite fields (FTFF) often occurs in an advanced abstract algebra course and invokes the power of Galois theory to prove it. Yet the combinatorial and algebraic coding theory applications of finite fields can show up early on for students in STEM. To make the FTFF more accessible to students lacking exposure to Galois theory, we provide a proof from algebraic "first principles."
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subjects Algebra
Binary system
Combinatorial analysis
Fields (mathematics)
First principles
Numbers
Students
Technical education
Theorems
title The fundamental theorem of finite fields: a proof from first principles
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